The image space of meyer wavelet transform

Abstract

Meyer wavelet is a classic wavelet, it has many good properties. For example derivation infinitely, smoothness, attenuates fast and its spectrum is finite, Meyer wavelet is beneficial to numerical calculate, so it applies widely in engineering majors. In this paper, we can discuss the properties of the image space of classic Meyer wavelet transform. According to the properties of reproducing kernel, In this space, we obtain the reproducing kernel function two expressions When scale factor is fixed. We also use the additive operation and norm operation of reproducing kernel space to describe the Meyer image space. This article provides one method about study the image space of the class of Meyer wavelets transform. In signal processing field, which is beneficial to choose wavelet base well. And in the actual application of the class of Meyer wavelet, by the results of this paper, in which can help us to choose a more suitable Meyer wavelet. We can give the optimal algorithm, programming by computer and develop the application software.